How can I make my custom templates respect permissions? in WordPress

Message you quoted is being generated by members_content_permissions_protect() function. By default it is used as a filter on the_content() and the_excerpt() functions. Since your custom template doesn use these - there is case for function to run.

Try something like this in template:

$content = 'Content to protect';
echo members_content_permissions_protect( $content );

Another idea:

$protected = members_content_permissions_protect( false );
if( false !== $protected ) { echo $protected;
}
else { //template stuff goes here
}